An SDD matrix \(A\)  has an equivalent characterization as a factor-with-two matrix, i.e., \(A = VV^{{\mathsf {T}}}\)  where each column of \(V\)  contains at most two non-zero elements [1]}. Furthermore,
\( A \!\in \! SDD_n \Leftrightarrow A \!=\!\!\! \sum _{1 \le i<j \le n} E_{ij}^{{\mathsf {T}}}M_{ij} E_{ij}, \text{with} \; M_{ij}\! \in \! \mathbb {S}^2_+,\) 
